Optical devices utilizing diffraction are well-known in the art. Such devices are often known as holographic elements. The most common holographic elements are transmissive to light. In such devices light receives a phase shift that is dependent upon the region of the device through which it travels. By carefully controlling the relative amounts of phase shift provided by different regions of the device, the diffractive properties may be controlled. An example of a transmissive diffractive element is a kinoform.
Although less common than transmissive diffractive elements, reflective diffractive elements are also known. For example, such a device is described in "Etchelette Zone Plates for Use in Far Infrared Spectroscopy" by A. Walsh, Journal of the Optical Society of America, March 1952, p. 213. Reflective diffractive systems are used primarily in situations where space limitations prevent the use of a conventional spheric or parabolic reflector. The alternative to a diffractive optical element in such a situation would be a conventional Fresnel-type reflector. If a precise focus is required, however, the Fresnel-type reflector will not provide adequate performance. This is because the presence of repeated Fresnel prisms will create diffractive effects, but without the precisely-controlled phase relationships of an element intentionally employing diffraction. The result is that the focus will be unacceptably diffuse. Alternatively a reflector intentionally employing diffraction can bring monochromatic light to a comparatively precise focus.
Another possible, although less common, use for a diffractive reflector arises when chromatic dispersion is desired in the image. Since conventional reflectors are achromatic, diffractive power is required to provide such dispersion.
A conventional diffractive reflector will have a series of linear or circular diffractive zones. These zones radiate outward from a central zone. For simplicity, such a device with circular zones will be described. Such a reflector has performance that corresponds approximately to that of a spherical mirror. Linear zones, providing performance that corresponds to a cylindrical reflector, or zones of arbitrary shape, will be understood by analogy.
In order to design a diffractive reflector, an object distance (D.sub.o) and an image distance (D.sub.i) are selected. The reflector will be designed such that light emanating from a point source, usually on the optical axis of the reflector, a distance equal to the object distance away from the reflector, will be brought to a point focus at a point also usually on the optical axis a distance away from the reflector equal to the image distance. In order to do so a series of concentric diffractive zones are formed on the surface of the reflector. The radii of the zones are given by the equation. ##EQU1## where n is the number of the zone counting from the center and the central is zone 0, r.sub.o is the radius of the central zone and .lambda. is the preselected design wavelength of the lens. The parameter f is equal to the reciprocal of the sum of the reciprocals of the object and image distances, i.e. ##EQU2##
The diffractive zones are separated from one another by optical steps. The optical steps should be of a size such that, for light emerging from the object point, a ray of light striking immediately on one side of an optical step will be phase shifted by one wavelength at the image point with respect to a ray of light falling immediately on the other side of the optical step. In general, optical steps equal to one half of the design wavelength will accomplish this. It should be noted, however, that, for wide apertures, trigonometric effects will require that the step heights be smaller.
Preferably each zone has a contour such that light starting from the object point, striking the reflector and arriving at the image point will have the same phase regardless of where the ray of light strikes the reflector within the zone, although some approximations are possible.
When the ratio of the parameter f to the aperture of the mirror is large, problems arise due to the size of the outer zones. First it is difficult to manufacture such zones because they become very narrow. Furthermore some scattering will occur from each of the discontinuities. Since the zones are very narrow in the outer region, there are more peaks in a given distance and, therefore, more scattering.